A note on the dissolution of spherical crystals

Abstract

We consider here the radial Stefan problem with Gibbs-Thomson law, which is a classical model describing growth or melting of a spherical crystal in a surrounding liquid. We shall specialize to the cases of two and three space dimensions and discuss the asymptotic behaviour of a melting crystal near its dissolution time t(*)>0. We prove here that, when the interface shrinks monotonically, the asymptotics near t=t(*) is of the form R(t)~(3σ(t(*)-t))(1/3), u(r,t)~-σ/r for r~R(t), r>R(t). Here, R(t) denotes the radius of the crystal, σ is a surface tension parameter and u(r,t) represents the field temperature. An important point to be noticed is that (*) exhibits no dependence on the space dimension N, in sharp contrast with results known for the case σ = 0.